Pert

1. Relationships
between Activities
• A project is a sequence of activities.
– Large projects have interrelated sequences.
• These are called Precedent activities
– They must be defined before the project
begins.

2. Step 2
Develop a Network Model
• A Network Diagram visually displays the interrelated
activities using nodes (circles) and arcs (arrows) that
depict the relationships between activities.
• It is a graphical diagram.
• Two types of Graphical Network Models
– Activity On Arc (AOA)
– Activity On Node (AON) (We will use AON)

3. Two Types
of Network Models
Activity-on-Arc (AOA)
Time Time Time
Activity D Activity E
Activity-on-Node (AON)
Activity Activity
We will use
D E this!
Link

4. What AON Nodes look like.
Slack (S) is the difference, if any,
The is the earliest you can start an
between the early start (ES) and late
activity. It is determined by the early
start times (LS) or the early finish (EF)
finish time of the precedent activity. If
and late finish (EF) times.
there are two or more precedent
activities, this time is the same as S = LS - ES or S = LF - EF
precedent activity with the latest “Early Slack
Finish” time.
The earliest you can complete an
activity--determined by adding the
Activity
activity time (duration) to the early
Early Early start time.
Start Finish
Late Late
This is the latest you can finish an
Start Activity Finish
Duration activity without delaying project
This is the Late-Finish completion. It is the same as the
time minus the activity Late Start time of the next activity.
duration. If there are two or more
subsequent activities, this time is
the same as the earliest of those
“Late Start” times.
© 2011 Lew Hofmann

5. Precedent
Relationships
Precedent relationships determine a sequence for accomplishing activities.
They specify that any given activity cannot start until its preceding activity or
activities have been completed.
Activity On Node approach
In our AON approach, the nodes (circles)
represent activities, and the arcs AON
represent the sequential relationships
between them.
S T U
Nodes are simplified in the following examples.
“S” precedes “T” which precedes
“U”

6. Activity Relationships
S & T must be completed T & U cannot begin until S
before U can be started. has been completed.
S T
U S
T U

7. Activity Relationships
U cannot begin until S & T have been
U & V can’t begin until S & T completed. V cannot begin until T has
have been completed. been completed.
S U S U
T V T V

8. Activity Relationships
T & U cannot begin until S has been
completed; V cannot begin until both T & U
have been completed.
S T V
U

9. St. Adolf’s Hospital
(A sample project)
Immediate
Activity Description Predecessor(s) *Responsibility
A Select administrative and medical staff. — Johnson
B Select site and do site survey. — Taylor
C Select equipment. A Adams
D Prepare final construction plans & layout. B Taylor
E Bring utilities to the site. B Burton
F Interview applicants and fill positions in A Johnson
nursing, support staff, maintenance,
and security.
G Purchase and take delivery of equipment. C Adams
H Construct the hospital. D Taylor
I Develop an information system. A Simmons
J Install the equipment. E,G,H Adams
K Train nurses and support staff. F,I,J Johnson
*We won’t be using the “Responsibility” data, but it is important in project management.

10. St. Adolf’s Hospital
Diagramming the Network
Activity Times
(wks)
Immediate I
Predecessors
A – 12 A F K
B – 9
C A 10
D B 10 Start C G Finish
E B 24
F A 10
G C 35 B D H J
H D 40
I A 15
J E,G,H 4 E
K F,I,J 6

11. St. Adolf’s Hospital
I
Paths are sequences of activities
between a project’s start and finish.
A F K
Path Time (wks)
Start C G Finish
A-I-K33
A-F-K28
B D H J
A-C-G-J-K 67
B-D-H-J-K 69
B-E-J-K 43
E

12. St. Adolf’s Hospital
The longest path is the critical path!
I
Path Time (wks) A F K
A-I-K33
A-F-K28 Start C G Finish
A-C-G-J-K 67
B-D-H-J-K 69
B-E-J-K 43 B D H J
Project Expected
Time is 69 wks. E

13. 3. Develop the schedule
• Now we insert the time estimates.
– This is where we distinguish between PERT & CPM.
• CPM is used when activity times are Certain.
• It is Decision making under Certainty
• You are certain of the time each activity will require to
complete.
• PERT is used when activity times are not certain.
(Decision making under risk)

14. Using PERT
• PERT is used when activity times are uncertain.
– Decision making under risk (“P” for probabilistic)
– Three time estimates are required for each activity.
• OPTIMISTIC TIME: Best time if everything goes perfectly
• REALISTIC TIME: Most likely time
• PESSIMISTIC TIME: A worst-case situation
B + 4M + P
Expected Time = -------------------
6
In this example, the most likely time is given a weight of 4, and the other two times (pessimistic
and optimistic) are each given weights of 1. Software allows you to change these as needed, but
the denominator must be the total of the weights given.

15. St. Adolf’s Hospital
Developing the schedule
• Earliest Start Time (ES) for an activity is the earliest finish time
of the immediately preceding activity.
• Earliest Finish Time (EF) for an activity is its earliest start time
plus how long it takes to do it (estimated duration).
• Latest Start Time (LS) is the latest you can finish the activity
minus the activity’s estimated duration.
• Latest Finish Time (LF) is the latest start time of the activity that
immediately follows it. (Latest start and finish times for each activity
are computed starting at the project’s last activity completion time
and working forward.)

16. Earliest Start and Earliest Finish Times
12
I 27
Earliest start time
15 Earliest finish time
A 12 K 69
0 12 F 22 63
12 10 6
12
C 22 22
G57
Start Finish
10 35
0
B9 9
D 19 19
H59 59
J 63
9 10 40 4
9 E 33
24
© 2012 Lew Hofmann

17. Earliest Start and Earliest Finish Times
Path Time (wks)
12
I 27 The Critical Path takes
A-I-K33 15 69 weeks
A-F-K28
A-C-G-J-K 67
A K 69
B-D-H-J-K 69 0 12 12 F 22 63
B-E-J-K 43 12 10 6
12
C 22 22
G57
Start Finish
10 35
0
B9 9
D 19 19
H59 59
J 63
Critical Path
9 10 40 4
9 E 33
24
© 2012 Lew Hofmann

18. Latest Start and Latest Finish Times
(Working from the last activity toward the first activity)
12
I27
48 1563
A K
0 12 12 F 22 Latest 63 69 Latest
2 1214 53 1063 start 63 6 69
finish
time time
C
12 22 22 G 57
Start Finish
14 1024 24 59
35
0
B9 9
D
19 19
H
59 59
J 63
0 9 9 9 1019 19 4059 59 4 63
9 E 33
35 2459
© 2012 Lew Hofmann

19. Node Duration ES LS Slack
Slack is the difference between LS
A 12 0 2 2 and ES or the EF and LF.
B 9 0 0 0
C 10 12 14 2
12
I27
D 10 9 9 0
E 24 9 35 26 48 1563
F 10 12 53 41
G 35 22 24 2
A K
H 40 19 19 0 0 12 12 F 22 63 69
I 15 12 48 36 2 12 14 53 1063 63 6 69
J 4 59 59 0
K 6 63 63 0
C
12 22 22 G 57
Start Finish
14 1024 24 59
35
0
B9 9
D
19 19
H59 59
J 63
Activity Slack 0 9 9 9 1019 19 4059 59 4 63
Analysis
9 E 33
35 2459
© 2012 Lew Hofmann

20. Sample Gantt
Chart Printout